Harvey Mudd College requires their math majors to take a public-speaking course specifically intended for math majors. From http://horizonsaftermath.blogspot.com/2014/04/every-math-major-should-take-public.html:
No matter what we all do after college . . . [we] will have to speak to people. Every one of us will have a limited amount of time that we can convince someone else to see our point of view.
I recommend reading the whole article.
Mean Green Math 
I’d only had one class somewhat touched on public speaking — a drama class, in high school — but it helped me considerably in going on to teach. It was good for shaking out stage fright, for one, and training me to move with purpose, and to avoid vocalizing my uh’s and uhm’s and other verbal tics. I could view teaching as partly playing the role of a teacher, after that.